{
  "figure_id": "fig04",
  "A": [
    1,
    2
  ],
  "trial_polynomial": "T_d((2*t-1)/3)",
  "definition": "R_d = -E[f*p_d(f)^2]/E[p_d(f)^2]",
  "status": "Exact rational trial values copied from round6/branches_78_83_results.json; decimals for plotting only",
  "hierarchy_relation": "R_d <= B_d <= K; R_d itself need not be monotone for arbitrary examples",
  "exact_target": "9/8",
  "values": [
    {
      "degree": 1,
      "R_exact": "1/5",
      "K_exact": "9/8",
      "gap_exact": "37/40",
      "R_approx": 0.2,
      "gap_approx": 0.925
    },
    {
      "degree": 2,
      "R_exact": "12/49",
      "K_exact": "9/8",
      "gap_exact": "345/392",
      "R_approx": 0.24489795918367346,
      "gap_approx": 0.8801020408163265
    },
    {
      "degree": 4,
      "R_exact": "4656/7201",
      "K_exact": "9/8",
      "gap_exact": "27561/57608",
      "R_approx": 0.6465768643243994,
      "gap_approx": 0.47842313567560063
    },
    {
      "degree": 8,
      "R_exact": "601297088/564810049",
      "K_exact": "9/8",
      "gap_exact": "272913737/4518480392",
      "R_approx": 1.0646005485642485,
      "gap_approx": 0.060399451435751636
    },
    {
      "degree": 12,
      "R_exact": "84674399485872/76148427919201",
      "K_exact": "9/8",
      "gap_exact": "7940655385833/609187423353608",
      "R_approx": 1.111965168548426,
      "gap_approx": 0.013034831451574106
    }
  ],
  "scope": "Not optimized B_d; not numerical evidence for an all-frequency convergence theorem; no optimality claim"
}